Originally Posted by plunet

99+% of the time you won't have a problem.

Provided that the name of the ticket resembles the name of the passenger there is usually no issue. Because the airline IT systems are built upon technology from years ago they are very inflexible with regard to name field and as such airlines understand this and minor typos, names being reversed or in the wrong order, punctuation missing, transliteration of non-western names causing names to be spelt differently are generally non-issues. You can Google something like 'airline ticket name misspelt' and get lots of independent confirmation.

Just to highlight how common reversed names can be, people of Chinese heritage would typically write a Chinese name as surname followed by firstnames. Therefore this issue occurs every day at check in counters.

Don't draw attention to the issue yourself whilst you are at the airport, and no one is likely to even query it.